US 7036097 B1 Abstract A method for designing a cascade of digital filters for use in the control of an electrolytic reduction cell by specifying the frequency and time response characteristics of the transfer function of the cascade of digital filters. The digital filters are exponential filters. The number of smoothing functions (i.e filters), each having different filter parameter values, is determined according to desired performance characteristics in the frequency and the time domains. These characteristics include: smoothing quality (specifiable in terms of passband, stopband and transition band of the filter frequency response profiles), group delay, and stabilization time. The use of the cascade of digital filters to control a reduction cell. A system for controlling a reduction cell comprising the cascade of digital filters. A process for electrolytic reduction of alumina comprising a step of filtering measurements of an electrical parameter using the cascade of digital filters.
Claims(19) 1. A method for designing a cascade of digital filters for use in controlling an electrolytic reduction cell, the cascade having a filter order corresponding to a number of digital filters in the cascade and each digital filter having a specifying parameter, the method comprising the steps of:
selecting a lowest value for the parameter for each digital filter such that each of a group delay and a settling time are within predetermined performance characteristics;
determining if a smoothing quality of the cascade of digital filters is within predetermined performance characteristics;
increasing the filter order by one when the smoothing quality is not within predetermined performance characteristics;
determining if a result of a time domain analysis is within predetermined performance characteristics; and
increasing the filter order by one when the result of the time domain analysis is not within predetermined performance characteristics;
wherein the filter order and the parameters for each of the digital filters is used to specify the cascade of digital filters to be used in controlling the electrolytic reduction cell.
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9. A method for designing a cascade of digital filters for use in controlling an electrolytic reduction cell, the cascade having a filter order corresponding to a number of digital filters in the cascade and each digital filter having a specifying parameter, the method comprising the steps of:
setting the filter order to one;
determining a group delay and a settling time as functions of parameter values for a predetermined sampling time;
selecting a lowest value for the parameter for each digital filter such that each of the group delay and the settling time are within predetermined performance characteristics based on the group delay and the settling time as functions of parameter values;
performing a frequency domain analysis for the cascade of digital filters;
determining if a smoothing quality of the cascade of digital filters is within predetermined performance characteristics based on the frequency domain analysis;
increasing the filter order by one when the smoothing quality is not within predetermined performance characteristics;
performing a time domain analysis for the cascade of digital filters;
determining if a result of the time domain analysis is within predetermined performance characteristics; and
increasing the filter order by one when the result of the time domain analysis is not within predetermined performance characteristics;
wherein the filter order and the parameters for each of the digital filters is used to specify the cascade of digital filters to be used in controlling the electrolytic reduction cell.
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18. A process for electrolytic reduction of alumina in a reduction cell, the process comprising the steps of:
introducing alumina into an electrolyte contained in the reduction cell;
applying an electric current between an anode and a cathode in the reduction cell;
measuring an electrical parameter representative of the alumina concentration in the reduction cell;
filtering measurements of the electrical parameter using a cascade of digital filters, the cascade having a filter order corresponding to a number of digital filters in the cascade and each digital filter having a specifying parameter, the filter order and the specifying parameters being determined by the steps of:
selecting a lowest value for the parameter for each digital filter such that each of a group delay and a settling time are within predetermined performance characteristics;
determining if a smoothing quality of the cascade of digital filters is within predetermined performance characteristics;
increasing the filter order by one when the smoothing quality is not within predetermined performance characteristics;
determining if a result of a time domain analysis is within predetermined performance characteristics; and
increasing the filter order by one when the result of the time domain analysis is not within predetermined performance characteristics;
predicting the onset of an anode effect based on filtered measurements of the electrical parameter; and
adding additional alumina into the electrolyte when the onset of an anode effect is predicted.
19. A system for controlling an electrolytic reduction cell comprising:
a mechanism for measuring an electrical parameter representative of an alumina concentration in the reduction cell;
a cascade of digital filters for filtering measurements of the electrical parameter, the cascade having a filter order corresponding to a number of digital filters in the cascade and each digital filter having a specifying parameter, the filter order and the specifying parameters being determined by:
selecting a lowest value for the parameter for each digital filter such that each of a group delay and a settling time are within predetermined performance characteristics;
determining if a smoothing quality of the cascade of digital filters is within predetermined performance characteristics;
determining if a result of a time domain analysis is within predetermined performance characteristics; and
a mechanism for predicting the onset of an anode effect based on filtered measurements of the electrical parameter; and
a mechanism for adding alumina into the reduction cell when the onset of an anode effect is predicted.
Description The present invention relates to the field of controlling the alumina feed to an electrolytic reduction cell. In particular, to a method for designing a cascade of digital filters for use in controlling an electrolytic reduction cell. The electrolytic reduction of alumina is normally carried out in a Hall-Heroult cell which comprises an elongated, shallow vessel lined with a conductor material, such as carbon, forming a cathode. The vessel holds a molten electrolyte, typically cryolite, containing a low concentration of dissolved alumina, and a number of carbon anodes dipped into the electrolyte from above. When a direct current is passed through the cell, molten aluminum is formed and descends to the bottom of the cell where it forms a pool acting as part of the cell cathode. As electrolysis proceeds, the concentration of alumina in the electrolyte falls and more alumina is added periodically. When the concentration in these regions falls to about 2% by weight or less, the so-called “anode effect” is observed. This manifests itself as a high voltage and the appearance of fluorocarbons in the anode gases. The anode effect is disadvantage for a number of well known reasons and attempts are made to avoid and/or terminate the anode effect. It would be highly desirable to be able to directly measure the alumina content of electrolysis cells. It is known to remove a sample from the electrolysis cell and analyze it for alumina content, but this is too slow to be commercially practical. Thus, most industrial processes have resorted to indirect evaluation of the alumina content by following an electrical parameter representative of the alumina concentration of the electrolyte. This parameter is generally a variation of the resistance at the cell electrode terminals such as a resistance trend (a.k.a. R-trend) indicator. The curve of the variation of resistance as a function of alumina content can be plotted by calibration and the alumina concentration can thereby be known. However, the measured resistance can be affected by factors other than the alumina concentration such as for example environmental (e.g. electrical) interference, perturbation generating phenomena, and other sources of noise which can be difficult to control or eliminate. Digital filters are used in a wide range of domains for signal processing and conditioning. In particular a cascade of multiple filters, such as Kalman filters, can be used for smoothing of a signal to remove or minimize the noise content in a measured signal. The individual filter parameters can be chosen, for example, based on observations made in the time domain. Digital filters have been used in the control of reduction cells to mitigate the impact of extraneous factors, such as those described above, on the resistance trend indicator. As the selection of filter parameters has typically been based on observations in the time domain, the impact of the filters in terms of attenuation as a function of frequency and other related performance characteristic is not generally known in these applications. Therefore, it has not been possible to predict the performance of the filters in the face of different phenomena (e.g. bubble noise, metal waves) that can occur in the reduction cell and affect measurement signals. What is needed is a method for designing a cascade of digital filters for use in controlling an electrolytic reduction cell that permits the performance characteristic (e.g. frequency response, stabilization time, group delay) of the cascade of filters to be adapted in light of knowledge of various types of phenomena that can occur in the cell. A method for designing a cascade of digital filters for use in the control of an electrolytic reduction cell by specifying the frequency and time response characteristics of the transfer function of the cascade of digital filters. The digital filters are exponential filters. The number of smoothing functions (i.e filters), each having different filter parameter values, is determined according to desired performance characteristics in the frequency and the time domains. These characteristics include: smoothing quality (specifiable in terms of passband, stopband and transition band of the filter frequency response profiles), group delay (to be minimized), and stabilization time (less than or equal a pre-determined value). The use of the cascade of digital filters to control a reduction cell. A system for controlling a reduction cell comprising the cascade of digital filters. A process for electrolytic reduction of alumina comprising a step of filtering measurements of an electrical parameter using the cascade of digital filters. In accordance with one aspect of the present invention, a method for designing a cascade of digital filters for use in controlling an electrolytic reduction cell, the cascade having a filter order corresponding to a number of digital filters in the cascade and each digital filter having a specifying parameter, the method comprising the steps of: selecting a lowest value for the parameter for each digital filter such that each of a group delay and a settling time are within predetermined performance characteristics; determining if a smoothing quality of the cascade of digital filters is within predetermined performance characteristics; increasing the filter order by one when the smoothing quality is not within predetermined performance characteristics; determining if a result of a time domain analysis is within predetermined performance characteristics; and increasing the filter order by one when the result of the time domain analysis is not within predetermined performance characteristics; wherein the filter order and the parameters for each of the digital filters is used to specify the cascade of digital filters to be used in controlling the electrolytic reduction cell. In accordance with another aspect of the present invention, a method for designing a cascade of digital filters for use in controlling an electrolytic reduction cell, the cascade having a filter order corresponding to a number of digital filters in the cascade and each digital filter having a specifying parameter, the method comprising the steps of: setting the filter order to one; determining a group delay and a settling time as functions of parameter values for a predetermined sampling time; selecting a lowest value for the parameter for each digital filter such that each of the group delay and the settling time are within predetermined performance characteristics based on the group delay and the settling time as functions of parameter values; performing a frequency domain analysis for the cascade of digital filters; determining if a smoothing quality of the cascade of digital filters is within predetermined performance characteristics based on the frequency domain analysis; increasing the filter order by one when the smoothing quality is not within predetermined performance characteristics; performing a time domain analysis for the cascade of digital filters; determining if a result of the time domain analysis is within predetermined performance characteristics; and increasing the filter order by one when the result of the time domain analysis is not within predetermined performance characteristics; wherein the filter order and the parameters for each of the digital filters is used to specify the cascade of digital filters to be used in controlling the electrolytic reduction cell. In accordance with still another aspect of the present invention, use of a cascade of digital filters designed according to the above described the method to control an electrolytic reduction cell. In accordance with yet another aspect of the present invention, a process for electrolytic reduction of alumina in a reduction cell, the process comprising the steps of: introducing alumina into an electrolyte contained in the reduction cell; applying an electric current between an anode and a cathode in the reduction cell; measuring an electrical parameter representative of the alumina concentration in the reduction cell; filtering measurements of the electrical parameter using a cascade of digital filters, the cascade having a filter, order corresponding to a number of digital filters in the cascade and each digital filter having a specifying parameter, the filter order and the specifying parameters being determined by the steps of: selecting a lowest value for the parameter for each digital filter such that each of a group delay and a settling time are within predetermined performance characteristics; determining if a smoothing quality of the cascade of digital filters is within predetermined performance characteristics; increasing the filter order by one when the smoothing quality is not within predetermined performance characteristics; determining if a result of a time domain analysis is within predetermined performance characteristics; and increasing the filter order by one when the result of the time domain analysis is not within predetermined performance characteristics; predicting the onset of an anode effect based on filtered measurements of the electrical parameter; and adding additional alumina into the electrolyte when the onset of an anode effect is predicted. In accordance with yet still another aspect of the present invention, a system for controlling an electrolytic reduction cell comprising: a mechanism for measuring an electrical parameter representative of an alumina concentration in the reduction cell; a cascade of digital filters for filtering measurements of the electrical parameter, the cascade having a filter order corresponding to a number of digital filters in the cascade and each digital filter having a specifying parameter, the filter order and the specifying parameters being determined by: selecting a lowest value for the parameter for each digital filter such that each of a group delay and a settling time are within predetermined performance characteristics; determining if a smoothing quality of the cascade of digital filters is within predetermined performance characteristics; increasing the filter order by one when the smoothing quality is not within predetermined performance characteristics; determining if a result of a time domain analysis is within predetermined performance characteristics; and increasing the filter order by one when the result of the time domain analysis is not within predetermined performance characteristics; a mechanism for predicting the onset of an anode effect based on filtered measurements of the electrical parameter; and a mechanism for adding alumina into the reduction cell when the onset of an anode effect is predicted. Other aspects and features of the present invention will become apparent to those ordinarily skilled in the art to which it pertains upon review of the following description of specific embodiments of the invention in conjunction with the accompanying figures. The present invention will be described in conjunction with the drawings in which: The present invention is directed to a method for designing a cascade of digital filters for use in the control of an electrolytic reduction cell by specifying the frequency and time response characteristics of the transfer function of the digital filters. The digital fiters are exponential filters arranged in a cascade. The apparatus A series of smoothed resistance values generated by the second smoothing filter The raw resistance, derived from voltage and current measurements for a given sampling period, is smoothed (i.e. filtered) using the smoothing filters The function, in the time domain, for a simple exponential filter, such as IIR filter Similarly, the transfer function, in the Z-domain, is described as follows: -
- R
_{f}(t)=the filtered resistance in discrete time - R
_{f}(z)=the z-transform of R_{f}(t) - R
_{raw}=the raw resistance - α=filter parameter (0<α<=1)
- Δt=the sampling period
- t=continuous time (0, ∞)
- k=the number of a sampling time (i.e. the k
^{th }sample) - z=the complex z-domain argument
- R
In the case of multiple simple exponential filters, the value of the filter parameters (e.g. α, β, γ, and ψ respectively for a four filter configuration) are determined by the placement of the poles and zeros in the Z-plane. Each simple exponential filter has an associated pole and a zero. The value of the pole is the difference between unity and the value of the filter parameter, for example the pole of the IIR filter A transfer function H(z), resulting from the convolution of those of the simple exponential filters, is used to effect a frequency domain analysis yielding the amplitude (or modulus) of H(iω), variation in the phase, and the group delay as a function of frequency. The profile of the amplitude of H(iω) as a function of frequency is an indicator of the quality of filtering of the resistance.
The determination of the filter parameters is based on the frequency and time domain performances (in response to step and impulse functions) desired according to imposed criteria. This approach allows the smoothed resistance to be generated, according to desired frequency and time domain performance characteristics, by adjusting the values of the filter parameters used. In order to fulfill the imposed criteria for the cascade of digital filters, the following conditions must be evaluated and met. -
- Condition 1: The group delay (delay of the filter response) must be within predetermined performance characteristics.
- Condition 2: The stabilization time or settling time must be within predetermined performance characteristics to take into account anode beam moves and other similar cell signal perturbations.
- Condition 3: The smoothing quality of the resistance indicator (i.e. the output of the cascade of digital filters) must be within predetermined performance characteristics (e.g. the magnitude of the passband and stopband in the frequency response and the width of the transition band) to ensure removal of the unwanted noise.
- Condition 4: The results of testing of the digital filters using simulations with signals sampled from cells (in extreme and normal conditions) must be within predetermined performance characteristics.
The method begins in step
In step In step In step If condition 3 is not satisfied, the filter order is increased by increasing the number of digital filters by one in step In step In step A cascade of digital filters A process for the electrolytic reduction of alumina in a reduction cell A system for controlling an electrolytic reduction cell It will be apparent to one skilled in the art that numerous modifications and departures from the specific embodiments described herein may be made without departing from the spirit and scope of the present invention. Patent Citations
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